The Basic Theorem of triadic concept analysis

Experiences with applications of concept lattices and the pragmatic philosophy founded by Ch. S. Peirce have suggested a triadic approach to formal concept analysis. It starts with the notion of a triadic context combining objects, attributes, and conditions under which objects may have certain attributes. The Basic Theorem of triadic concept analysis clarifies the class of structures which are formed by the triadic concepts of triadic contexts: These structures are exactly the complete trilattices up to isomorphism.